TABLE 79.-Of the CONNECTION between the ultimate TRANSVERSE STRENGTH of MATERIALS, and the TENSILE, and CRUSHING STRENGTHS. Cast Iron 16,000 | 96,320 6.02 2063 Stirling's No. 2 25,764 119, 457 4.64 2835 No.3 23,461 129,876 5:54 2272 Wrought Iron: working) load 23,940 23,940 1.00 1330 Steel : working load €0,480 60,480 1.00 3360 Gun-metal 31,360 | 34,652* 1.105 1830 Brass 17,970 24,000* 1.335 1150 Glass 2,560 30,150 11.78 262 Slate 2,666* 12,062 4:52 421 Alder 14,186 6,896 • 485 530 Ash 16,576 9,023 •544 681 Beech 14,822 8,548 •577 558 Deal 17,850 6,602 .370 615 Larch 9,560 4,385 •459 380 Mahogany 10,818 8,198 • 758 589 Oak, English 12,332 8,271 • 670 509 Pine, yellow .. 13,300 5,410 •407 428 491 13,300 6,790 *510 577 Sycamore 13,000 8,144 .626 535 Teak 15,090 10,706 • 709 724 Willow 13,250 4,513 • 340 365 (1) (2) (3) 1795 - 15.0 2666 - 6:0 2568 +13:0 1330 0.0 3360 0.0 1830 0.0 1150 0.0 340 +30:0 421 0:0 545 + 2.85 673 - 1.17 613 +10.00 567 - 7.8 346 - 9:0 514 -12.73 556 + 9.2 448 + 4:7 498 + :4 514 - 10.92 566 + 5.8 700 3.32 347 4.93 (5) (6) NOTE -The values marked * have been calculated from the transverse strengths in col. 4, &c., &c. tions. The sum of all the + errors in col. 6 is 76.95, and of the - errors is 70.87, giving an average of (76.95 – 70-87) • 22 = + 0.276 per cent on the 22 experiments : the greatest + error was + 30 per cent. with Glass, and the greatest error was 15 per cent. with Cast Iron. (509.) It will be interesting and instructive to observe the effect on the transverse strength, of variations in the Tensile and Crushing strengths :—for instance, if by mixture of metals or otherwise we could double the value of both strains, no doubt the transverse strength would be doubled also; but the question is, what would be the effect of a given alteration in one of those strains only? Table 80 has been calculated by the rules in (496), &c., and shows the effect of changing the value of T and C from 7 and 42 tons per square inch respectively (which are nearly the mean strengths of ordinary cast iron) to 14 and 7 tons. Thus if T could be doubled or increased to 14 tons, while C remained at its normal value of 42 tons, the increase in the Transverse strength, as shown by col. 5, would be 63.3 per cent. If, on the other hand, with T at its normal value of 7 tons per square inch, C is reduced to 7 tons also, the transverse strength would be reduced to • 4962, or about half its normal value; when, as in (500) and (638), the transverse strength is sth of T or C; for by col. 4, .389 x 18 = 7 tons, &c. A practical example of this is given by Stirling's iron in (939), where it is shown that the effect of Stirling's process is to increase the tensile strength 74 per cent., and the crushing strength 30 per cent., the result being an increase of 60 per cent. in the transverse strength by experiment, and 59 per cent. by calculation with the rules in (496), &c. TABLE 80.-Of the TRANSVERSE STRENGTH of Cast Iron, &c., as THEORETICAL RULES. (510.) Theoretical writers have given rules connecting the transverse strain on a beam with the tensile and crushing strength of the material, based on the assumption that the two latter are equal to one another, and that the extensions and compressions under those strains are also equal. This, however, is not true of any material (616) when the strains are very heavy or approach the breaking weight; but with the working loads commonly adopted in practice, say {th to ļrd of the breaking weight, those rules are nearly correct, and become of considerable value. With very heavy strains other rules become necessary, and are given in (323). (511.) For solid square sections of beams we have the rules : affected by varying Tensile and Crushing Strength. Transverse Strength. Tensile, Crushing, Ratios. Ratios. Lbs. Tons. 7 14 21 28 35 871 1195 1400 1548 1664 1756 1926 2258 2538 2867 7 8 10 12 14 (1) 42 42 42 42 42 (2) . 3890 • 4962 .5344 -6816 .6251 •7973 6909 .8812 • 7427 .9473 •7840 1.0000 .8600 1.097 1.008 1.286 1.133 1.445 1.280 1.633 (5) 1.000 1.372 1.674 1.777 1.911 2016 2.211 2.592 2.914 3.291 (6) f x 2 x DS 3 xl W = . (514.) For hollow Rectangular sections : f * 2 * {D® x B) – (4 x 0} 3 xl xD W = (516.) For hollow circular sections : 3.1416 RX7 W = WXlXR f= 3.1416 (R'- p) W = (517.) For solid elliptical sections 3.1416 xf x R Rg 1 W X1 f = 3.1416 X R; X RB W = (518.) For hollow elliptical sections : 3.1416 * f * {R} x Rm) – (** **s} 1x RD WXlx RD f= 3.1416 * {R} x Rx) – ("% X Ps} In which f = the maximum strain per square inch at the extreme upper and lower edges of the section, usually tensile at the lower edge and crushing at the lower one, and in the same terms as W. = W = the transverse load in the centre of a beam supported at both ends in lbs., tons, &c., including the weight of the beam itself reduced to an equivalent central load (785). D = the external and d = the internal depth in inches. B = b breadth R radius 1D radius or ver tical semi diameter. RB = TB= radius or hori zontal semi diameter. 1 the length or distance between supports, in inches. RD = = or (519.) We may now give some illustrations of the application of these rules :-Say we have a bar of wrought iron 1 inch square and 1 foot long, and assuming that the maximum strain f shall not exceed 12 tons per square inch,-which, as shown by the Diagram 215, is about the limit of perfect elasticity for both the tensile and compressive strains, we may find the equivalent 12 x 2 = 1 transverse strain W by rule (511), which becomes 3 x 12 24 = .6667 ton, or 1500 lbs. in the centre. 36 If the bar had been a round one, then R = 0.5, and .53 3.1416 x 12 x 125 being •125, Rule (515) becomes = .3927 12 ton in the centre. Hence the ratio of the strengths of square to round bars is .6667 ; •3927 1.7 to 1.0. This is probably the correct ratio for light strains, and nearly so for all strains with materials whose elasticity is nearly perfect, such as steel and wrought iron, but with cast iron and timber, as shown in (361), (362), the ratio with the breaking weights is more nearly 1.5 to 1:0. (520.) By col. 6 of Table 66, the working load for a plain bar of wrought iron 1 inch square and 1 foot long = .594 ton in |